POLITECNICO DI TORINO
Master’s Degree in Civil Engineering
Master’s Degree Thesis
Study of a lightweight structure in the mountains with two different materials through the Building Information Modelling
Tutor
Prof. Anna Osello Co-Tutor
Prof Gabriele Bertagnoli
Candidate
Matthias Kather
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Abstract
The building of high alpine environment facilities is certainly a current topic in a society that has seen in recent years a rapid increase in mountain tourism; in modern times, many interesting different types of new solutions are found and applied for these constructions whose priorities are, for the conditions they are built in, lightness, high resistance, high thermal insulation and also aesthetical fitting with the surrounding environment; for these purposes, the in most cases best satisfying material is wood, which can have different applications and come in different forms; one of them is the Structural Insulated Panel (SIP).
SIPs are, as the name suggests, panels that can have a structural function in a building and, if wood based, their composition consists in two timber sheets and an insulating core. They arise as a composite material potentially able to provide with excellent thermal performances and at the same time additional stiffness to strengthen the whole structure and possibly decrease, or in some cases also completely replace the presence of frame elements. In recent years, innovative types of SIPs with various sorts of wood and different thicknesses of the layers have been developed in order to try to further improve their performances, but on which, due to their young age, not much is known.
Especially in Italy, where timber framing and crosslam panels are the most common wood construction systems, little information is present in literature about SIPs and their structural behaviour.
The current thesis aims to do a research about two different Structural Insulated Panel types in order to collect as much information possible about them and then create an accurate digital model of a high mountain building, more precisely a bivouac, employing those panels.
To reach this goal, Building Information Modelling methodology and its software have been used, which have proven to be a very useful tool for the collection of high amounts of intelligent data in one or more programs and then creation of digital models reproducing real-life products.
The building modelled in this thesis in not an existing bivouac but a project, present currently only in the form of drawings which were made and handed to me by the Leap Factory company.
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Table of contents:
Introduction………...….6
Chapter 1: General introduction to bivouacs and BIM, territorial and structural framework of the case study……….………..8
1.1 Historical background of bivouacs……….….8
1.2 State of Art………...……….11
1.2.1 Transportation………..………...………...11
1.2.2 Foundation and structure………...………...12
1.2.3 Claddings and openings………...…………..13
1.2.4 Spatial organization and technological aspect………13
1.3 Brief introduction to Building Information Modelling………..14
1.3.1 Background………...……….14
1.3.2 General information ………...…………...15
1.3.3 Interoperability………...…………18
1.3.4 BIM today………...…………...18
1.4 The case study………...………20
1.4.1 Structural framework………...………..21
1.4.2 Setting of the structure………23
Chapter 2 2D BIM: description of the structural panels and definition of the loads on the structure………24
2.1 What are SIPs?...24
2.1.1 Benefits and drawbacks………..25
2.2 The KINGSPAN system………...26
2.2.1 Mechanical properties………28
2.2.1 Thermal performance……….30
2.2.3 Vapour diffusion and condensation risk……….32
2.2.4 Connections………...35
2.2.5 Costs………..38
2.3 The Panelo system………...………..38
2.3.1 Mechanical properties………39
2.3.2 Thermal performance……….42
2.3.3 Vapour diffusion and condensation risk……….44
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2.3.4 Connections………...………45
2.3.5 Costs………...………...47
2.4 Initial comparison………..………...48
2.5 Definition of the loads on the structure………..49
2.5.1 Wind………..49
2.5.2 Snow………...………...53
2.5.3 Temperature………...………54
Chapter 3 Creation of the 3D models and software interoperability……….58
3.1 The initial steps: Revit, Robot and SAP2000……….58
3.2 The Dlubal structural model………..60
3.2.1 The panel………60
3.2.2 The geometry……….64
3.2.2.1 Structure with Kingspan TEK Panels………..64
3.2.2.2 Structure with Kingspan Panelo Panels………...………69
3.2.3 The panel connections………71
3.2.3.1 Kingspan Panels………...………...72
3.2.3.2 Panelo Panels………...………...77
3.2.4 The frame connections………...78
3.2.5 Application of the loads……….….84
3.2.5.1 Snow loads………...……...84
3.2.5.2 Wind loads………...………...85
3.2.5.3 Temperature………...………….86
3.2.5.4 Limit States combinations………...…………....87
3.3 The Revit model………90
3.3.1 The panel………90
3.3.2 The spline connections………...92
3.3.3 Final Geometry………..94
3.4 Interoperability………..97
Chapter 4 Results: Structural analysis, thermal performance, interstitial condensation and costs………..100
4.1 Structural Analysis………..100
4.1.1 ULS………..100
4.1.1.1 Kingspan structural model………100
4.1.1.2 Dlubal structural model……….104
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4.1.1.3 The problem of the singularities………108
4.1.2 SLS………..108
4.1.2.1 Kingspan structural model………108
4.1.2.2 Panelo structural model……….112
4.2 Thermal performance………..114
4.3 Surface condensation………..115
4.4 Costs………...121
4.5 Final comparison……….………122
Conclusion and future works……….124
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Introduction
Extreme environments have always been, throughout the history of humankind, a symbol of challenge and exploration, which eventually led, in some cases, to new discoveries and improvements of the society. In the case of building engineering it’s no different; the hostile climatic conditions that are to be found when building in glacial or oceanic ambiances present difficulties that often require a deep attention of the single case study, in order to allow the structure to “survive” those conditions.
In this context, in recent years, particular effort has been put in the research of h ow to optimize structures situated on high altitudes in the mountains, as those territories have seen a more and more increasing anthropization in the past decades and centuries. This is probably due to many factors, such as the growth of interest for this environment for the practice of sports, as a place where to escape to from the usual city life, but also at times to the improved accessibility these locations have because of climate changes (e.g the retreat of glaciers, phenomenon often observable in the Alps).
One type of structure that has its “natural habitat” in these types of surroundings is the bivouac. It is a usually small and lightweight construction, which purpose is originally not to be called “home” by some inhabitants, but to offer shelter f or those who need it. Therefore, generally these structures provide only with the bare essential, i.e. walls, roof for protection and a bed. Given the utmost challenging forces of nature to which they are subjected and the remote sites they are located in, bivouacs potentially represent an ideal “…laboratory, of experimental nature, where to put to test, in an environmental context close to the limits, central issues of modern a rchitecture: prefabrication, new materials, lightness related to stiffness, short times of building sites, but also the relation between the object the and alpine environment,…” (Dini, Gibello, Girodo, Hoepli ed., 2018, translation by M.K.).
The above-mentioned issues require, for their often-complex nature, new and more effective approaches to study and solve them. One of them is offered, in the modern era, by the BIM (Building Information Modelling) methodology. The Building Information Modelling was developed in recent years, and it includes various tools (most of them consisting in computer files), which can be used and modified by one or more people and then exchanged, extracted or networked in a process of collaboration between professionals of different sectors of the construction industry. It has led to drastic changed in the engineering world, regarding the designing phase but also the construction and maintenance phase. Its basic concept consists in the realization of a digital model of the structure containing information about the characteristics of the latter, which allow it to work as a digital repository of the real building during its entire life cycle.
7 The aim of this thesis is to analyse a lightweight structure in the mountains, a bivouac, made with two different wood based structural insulated panels, in order to make a structural, energetic and cost based research and then comparison of the two construction systems. The study has been dealt with using the BIM methodology, with the purpose of creating a digital model of the building working with various software, to try to reach a high amount of information within the model and to put to test the interoperability amongst them.
The work is divided in 4 chapters: in the first, there will be a brief illustration of the history and the state of art of the bivouacs, an introduction to BIM, as well as a description of the territorial organization of the case and of the architectonical and structural shape of the structure. The second will display the used construction systems, meaning a detailed illustration of the two kinds of composite materials and the main differences between them, and the definition of the loads acting on the structure. The third chapter exposes the creation of the 3D BIM models of the specific case study, including a suggested solution of a structural model for both panels and a more architectonical model, and will examine the interoperability between the employed software. Finally, the fourth chapter exposes the obtained results regarding the structural, energetic and costs analysis.
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Chapter 1 General introduction to bivouacs and BIM, territorial and structural framework of the case study
1.1 Historical background of bivouacs
When speaking about facilities providing shelter in high alpine environments, there are essentially two kinds that can be the taken into account. The most famous and relevant one is probably the mountain hut, which typically is a big structure able to, during summer season, host a relatively large amount of people, who usually are paying clients and get offered a service in the form of beds, served food, running water and a heating system by a staff living and working in the building. The second kind consists in the bivouac, a much smaller and simpler construction that is normally free for everyone and that doesn’t provide with any sort of comfort. Bivouacs are generally composed by one or maximum two rooms that can contain tables, chairs, beds and possibly other kinds of supplies that can vary from case to case depending on the function and use of the bivouac.
Those two different types of construction have in common the primary necessity of “hosting people in a domesticated space, in the least habitable areas of Europe.” (Dini, Luca Gibello, Stefano Girodo, Hoepli ed., 2018, translation by M.K.). They are the result of a relatively recent phenomenon, widespread throughout Europe, that consisted in the “conquest” of the highest peaks of the Alps by alpinists. It started in the late 18th century, (in fact, the first mountain hut, called “Temple de la Nature”, was built in 1795 in Montenvers, on the Mont Blanc massif), and reached its peak in the second half of the 19th century, during the so called “golden age” of alpinism between 1854 and 1865, when the alps were considered to be “the playground of Europe” (“The playground of Europe”, Stephen L., Longmans, Green, and Co., London, 1871).
Figure 1.1: Drawing by Charles Vallot, illustrating the “Temple de la Nature” in its original shape.
9 In these years, in the midst of the mountain enthusiasm caused by these big ascents, also the first alpinism organisations and clubs were born in many countries throughout Europe; in England the Alpine Club was founded London in 1857, followed by similar associations other countries, such as Switzerland, Austria and Italy, where the Club Alpino Italiano (CAI) was founded in 1863. It is thanks to the CAI that, in Italy, a more or less organized construction of a net of bivouacs in the Italian territories of the Alps was conducted in the 1920s-1930s. The designing of most of them was entrusted to the brothers Rivera from Turin, whose typical structure model was, as illustrated in Figure 1.2, of semi-cylindrical form, with a height of 1.25m at the ridge, and 2.4 by 2 m base dimensions.
Figure 1.2: The “model Rivera”, source Historic Archive of the CAI, Biblioteca Nazionale del CAI di Torino
The materials involved in those constructions where all easily mountable and removable, and lightweight, in order to be transportable by mules. As can be observed in figure Figure 1.2, the structure was in wood and had a cladding consisting in sheet metal made of zinc, internally covered with wooden boards covered by a layer of bituminous waterproofing. It could contain up to four people.
Dimensions grew and the form slightly changed during and after the second world war; this period saw, in Italy, two main very similar models designed one by the engineer Apollonio and the other one by the engineer Baroni, with the help of the Berti foundation. As can be seen in Figure 1.3, the semi- cylindrical shape was abandoned and replaced by bigger structures able to host more people (up to nine). Above in the figure, drawings of the Apollonio model show the typical arch of variable radius shaped roof, leaning on vertical walls that allowed the structure to reach heights of about 2.30 m. In the Berti-Baroni model, shown below in the figure, the slight difference can be observed in the roof;
10 it is formed by six sides of equal length but different inclination. The base dimensions (2,82x2,28m) as well as the materials on the other hand remained in both cases very similar to the model Rivera.
The model Apollonio and the model Berti-Baroni are until today the most replicated models in the history of high altitude constructions.
Figure 1.3 The Apollonio model (above) and the Berti-Baroni model (below). Source Historical Archive of the CAI, Biblioteca Nazionale del CAI di Torino
With the economic boom between the late 60s and 90s, a new revolution in the design of these structures took place. The newfound welfare allowed big steps forward in the progress of the technologies related to materials and construction techniques, resulting in highly technological buildings with futuristic shapes, perfectly reflecting the historical period they were built in, in which humanity was parallelly beginning to explore space. Although, differently to the previous cases, those configurations remained always experimental and were never replicated.
Figure 1.4 Above from the left: Bivacco Adolfo Hess (Rivera Model), built in 1925; bivacco Ivrea (Apollonio mo del), built in 1948.
Below: two examples of futuristic shaped bivouacs from the 60s to 90s period. From the left: bivacco Bruno Ferrario, built in 1968 and bivouac du Dolent-La Maye built in 1973.
11 Nowadays there’s an estimated two thousand (or more) structures considering mountain huts and bivouacs spread over the alpine territories of Italy, France, Monaco, Switzerland, Germany, Liechtenstein, Austria, and Slovenia. This high number translates in a large variety of architectonical and structural approaches regarding shapes and involved materials which, as seen in the paragraphs above, has gone through a big evolution in time, leading to today’s situation.
Figure 1.5 Evolution of the shape of the bivouacs in time
1.2 State of Art
1.2.1 Transportation
The construction sites are normally located in faraway areas, isolated and very hard to reach. It is therefore generally a good rule to maintain the construction times as short as possible; ice, snow and freezing cold temperatures which in some cases affect the site for twelve months a year, surely appear in large quantities or, when already present, increase during the winter season. In this context, a massive progress was brought in recent years by the establishment of the helico pter as a transportation tool, replacing the previously used mules or human shoulders. A revolution that allowed, apart from drastically reducing the construction times, many more possibilities not only in the involved materials but also in technical solutions, as the helicopter can work not only for the shipping of material but also for the assembly of heavy pieces together. Nevertheless, despite the obvious advantages implicated by its use, the aircraft transportation is a mean that still presents limits; the maximum weight capacity of a single helicopter is depending from various factors, but usually has an average of about 900 kg, corresponding more or less to that of a lorry. In some cases, in recent years, the solution taken has been that of designing extremely lightweight and small structures whose total weight was within those limits.
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1.2.2 Foundation and structure
For what concerns the foundation, obviously the employment of materials such as concrete or steel represent an enormous obstacle with a view of a possible transportation of those, as an operation of that kind could become very expensive. With this in mind, it is often an adapted solution to choose a position which characteristics allow it to at least partially avoid the implementation of this part of the structure. This condition can occur in situations where the ground is already of extremely good quality, and it’s enough to place wooden or metal spars on it, or when there are already pre-existing base plates. In case a foundation has to be built, an efficient solution is to place punctual concrete plinths, allowing to have a small digging surface so to minimize the damage to the ground. In addition, it is always appropriate to elevate the structure from the ground in order to better isolate it thermally.
Figure 1.6 From left to right: Plinth foundation of the Jubiläumsgrat bivouac; Bivacco Gervasutti, built in 2 011
The structure itself has to face the massive challenge of being able to withstand the, in these environments, very big wind and snow loads, and at the same time being as lightweight as possible for the previously mentioned limitations imposed both by the transportation as well as by the lack of real mechanical lifting arms. The material that best suits the combination of those conditions is without a doubt wood, which is also usually the best solution from an aesthetic point of view, as it reduces to the minimum the contrast between nature and building. It has a high versatility in terms of processing, a good structural and thermal performance and is fairly durable and light; it is mostly used in the form of frame and panels. Other solutions adapted in recent years resorted to the metallic carpentry or in some cases to synthetic materials like plastic or fiberglass; an example of the latter would be the Gervasutti bivouac (Figure 1.6, right) on the Mont Blanc massif.
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1.2.3 Claddings and openings
The external cladding, which has as primary function that of protecting the structure from atmospheric agents, is mostly used in its metallic forms; copper, sheet metal and aluminium are often adapted solutions. Internally, the most common cover is wood or plastic based. Is it important for these components to be light and easily installable, and for the internal claddings the vapour resistance can be a factor of significance in order to avoid interstitial condensation.
Given the original function of a bivouac, that is not designed for a visitor to stay for more than a certain amount of time, openings are usually a secondary element in the building. In general, it can be noticed that while in the past it was not uncommon to see a use of windows reduced to its minimum, today the tendency is to widen their surface in the construction (as can for example be seen in the Gervasutti bivouac, Figure 1.6, right), so as to “bring” the surrounding environment inside the bivouac. This is probably due to a phenomenon that started in recent years and is still ongoing today, which consists in a radical change of the approach towards these structures, as they are in many cases seen less and less as “only” a necessary shelter on the way of climbing before unreached peaks, and more as a “destination” in themselves. Therefore, the attention to the aesthetical aspect and the effort put in their design is much higher today than it was one century ago.
1.2.4 Spatial organization and technological aspect
As bivouacs are such small and essential buildings, the spatial organization plays a vital role in their assessment. A functional solution is to have one space with beds developing vertically, in order to optimize the space at the base; nevertheless, in the last years, more and more biv ouacs are built with more than one space, significantly increasing their dimensions with respect to less recent times.
The technological equipment of the structure represents in today’s time a new type of challenge and is at the same time a largely discussed matter in the high mountains world. On one side, those who have a more conservative view of alpinism and of the use of bivouacs favour a spartan type of configuration, refusing any type of possible technological progress; on the other side, the convinced innovators call for as much technological comfort as possible. Generally, it is today common to have a “basic set”, provided with a small photovoltaic panel able to produce enough energy to feed a radio transmitter for SOS. Furthermore, a few constructions nowadays are equipped with additional supplies like a mechanical air circulation system, internet connection or a heating system. Those gadgets, as much as they can increase the quality of the permanence inside bivouacs, have the problem of requiring a lot of maintenance, which makes them often expensive and little practical.
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1.3 Brief introduction to Building Information Modelling
Building Information Modelling, commonly referred to as “BIM”, is as of today probably one of the hot topics in the construction world. A real milestone, considering the context in which it was born and the changes it eventually contributed to in the approach towards many aspects of the industry.
Various definitions have been given to BIM; one is suggested by Eastman et al., 2008 in “BIM Handbook”, where BIM is described as “a verb or adjective phrase to describe tools, processes, and technologies that are facilitated by digital, machine readable documentation about a building and its performance, design, construction and operation”. As the definition insinuates, BIM touches many sectors of the whole building process, and is therefore perceived in different ways from people from e.g. the design, construction and financial management field. In fact, BIM today refers to a product (the building information model), a process (the creation of all the intelligent data that can be used throughout the lifecycle of the construction, building information modelling) and to a system (the management of the net of data and files useful to increase quality and efficiency, building information management). One could say that, in a nutshell, the ultimate goal of BIM is to improve and maximize the design efficiency and the management of a project; this is done through the employment of digital modelling software that allow to have all the information needed in one single virtual building model which can be linked to numerical data, texts, images and other type of information, accessible and modifiable by all different professionals involved in the construction process.
1.3.1 Background
The construction sector employs 7 per cent of the world’s working population and is one of the largest sectors in world economy, with about 10 trillion dollars spent on construction related goods every year, equivalent to 13 percent of Gross Domestic Product (McKingsey&Company, 2017). However, according to a study conducted by the McKingsey Global Institute in more than 20 countries and 30 companies, construction has suffered in the past decades from poor productivity relative to other sectors; compared with a 2.8 percent growth average per year for the total world economy and a 3.6 percent for manufacturing, construction sector labor -productivity growth averaged 1 percent per year over the past two decades. The labor-productivity performance of the construction sector is not equal throughout the world and there are obviously regional differences, with better and worst performing countries. For example, always refering to the analysis performed by McKingsey, in the United States the labor-productivity of the branch is lower today than it was in 1968.
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Figure 1.7 Productivity of construction industry in comparison with the manufacturing industry and the total economy
One of the main causes for these issues, is that many construction projects suffer from overruns in cost and time. In fact, for any type of civil construction project there are tens to hundreds of documents, blueprints and details that must be followed and interpreted, and this number can increase even drastically in the case of a major infrastructure projects. This high number of data combined with the oftentimes complicated communication taking place between the different parts involved in the project result in many situations in delays in the construction times, unexpected high field costs and also legal problems.
In this context, BIM can be an extremely useful tool in order to facilitate not only the creation of the various information concerning a construction i.e. drawings, schedules and specification details which are all contained in one digital model, but also the interaction between people from different fields of the building industry having to collaborate for the project.
1.3.2 General information
Being BIM, as seen in the previous paragraphs, such a multitasking tool, the question often arises of what exactly BIM is. In fact, a common mistake is to speak of BIM as of purely a set of software able to create a model. Probably, a more appropriate way to refer to BIM is of a methodology integrating all the professionals involved in the construction process (architects, engineers, contractors, etc) and creating a flow of information between them thanks to a representation of “both the physical and intrinsic properties of the building as an object-oriented model tied to a database” (Quirk, 2012).
Important features of BIM are listed below:
16 - All BIM software are able to update information automatically; this means that, as the model is developed, all other drawings within the project are adjusted accordingly without the need of any further intervention. This is particularly useful to reduce the times of the operations and avoid the human error when they are performed.
- The different parts involved in the project all work on the same model. This allows for a more fluid workflow and minimizes the loss of information during the process.
- The model is accessible and useful throughout every life-cycle phase of the structure or infrastructure, from the initial conceptual planning and designing phase to the in -operation maintenance, form the building phase to even the eventual deconstruction phase; this is an enormous simplification with respect to any other previous existing method, where all o f those issues were in many occasions newly approached, making it often very complicated to know th e necessary information about the building, for example in the case of maintenance, in order to operate.
- Since the model is accessible to professionals of different construction fields, everyone can add what for them is most essential for the project making it the closest thing to what can be a complete representation of reality.
Every BIM model is developed in different so called “dimensions” that describe the levels of information of the model, which will now be listed and explained:
- 1D, the idea:
The first phase usually consists in a first vision of the project to be done; a location is defined, as well as the function of the to-build construction and possibly a qualitative first estimation of the order of magnitude of the project (how many people are involved, costs etc).
- 2D, drawings:
The second dimension consists in the two-dimensional (x-y axis) drawings. Further information to be added can be the materials involved, the definition of a structural scheme and the applied loads.
- 3D, model:
The z axis is added in the third dimension, and a three-dimensional model is created based on the information collected in the first two dimensions. This is, perhaps, the most commonly known kind of BIM, a concept that many are familiar with. The model however is not static, it evolves in time with the adding of more and more details and information. The final model is the “As-built” one, giving ideally a precise representation of the real product.
- 4D, the time element:
17 4D BIM adds an additional dimension to the project data in the form of time scheduling of the different operations and construction phases. Information like the construction times or the order of installation of the different components can be added here, resulting in improved control over conflict detection or over the many changes occurring during a construction project.
- 5D, the costs:
The fifth dimension adds the component of the costs to the whole procedure. This variable is updated regularly on the software and allows users to visualise regularly where they stand cost-wise in the project and estimate the overall costing associated to the progress of the activities. Compared with the traditional methodology, where the costs aren’t updated as regularly, cost managers will have to start operating earlier and perform more iterations but this will result in better outcomes, as it will make it easier to remain in the initially defined budgets.
- 6D, sustainability:
This dimension is used to assess the energetic performance of the construction during its operational phase. Sensors should allow to collect the needed data in order to define a strategy aiming to optimize the facility’s energy consumption.
- 7D, facility management:
7D is where the BIM data can definitely make a difference. In fact, the operation and maintenance of a construction, that this dimension regards, can signify an important percentage of the total accumulated costs of a building during its life cycle, and starting a facility management program based on reliable data extracted from a well made as-built BIM model provides with the most effective solutions for the management of a construction.
Figure 1.8 Level of Detail descriptions
18 Furthermore, all BIM models are characterised by a Level of Detail (LOD), that basically describes the quality of the model, in terms of total amount of information contained. This value usually starts at 100 at the very early stages of the procedure and increases over time with the progress of the project, eventually reaching maximum quantity of 500, that represents the As-built model containing all the possible information. An idea of the difference between the various LODs is given in Figure 1.8.
1.3.3 Interoperability
Interoperability is a very important aspect of BIM Software and of BIM in general. When creating a BIM model, it may be necessary at times to transfer data from one software to another in order to increase the amount of information of the model. In fact, some software may be specialized in some types of operations but lacking at possibilities in others, which on the other hand can be better handled by different products; interoperability should grant the opportunity to perform every operation with the best fitting tool, so to have the most complete model possible. It is therefore important that during this process the least amount of data goes lost. Additionally, one always has to take into account the limitations imposed in this case by the costs, since these software usually have a relatively high price.
However, interoperability is ultimately defined by the ASUL interoperability working group as “a characteristic of a product or system, whose interfaces are completely understood, to work with other products or systems, present or future, in either implementation or access, without any restrictions”.
As will be noticed, it is described as a characteristic of the tool, and not as a process.
Since poor interoperability can represent a big obstacle to the progress of the project and possibly be the cause of financial losses, neutral, non-proprietary or open standards for sharing BIM data among different software applications have been developed in order to achieve the best outcome. Examples of BIM standards are the CIMSteel Integration Standard (CIS 2), which enables data exchange during the design and construction of steel framed structures, Construction Operations Building information exchange (COBie), useful particularly in the operation and main tenance phase, and finally the probably most known Industry Foundation Classes (IFC), developed by buildingSMART and recognised by the ISO. The latter has been an official standard, ISO 16739, since 2013.
1.3.4 BIM today
Nowadays, the implementation of BIM is spreading and increasing rapidly throughout the world. In the United Kingdom, undisputed world leader in the branch, the British Standard Institute (BSI) has
19 strongly promoted the utilization of the methodology in recent years by producing various standard (BS 1192) to support the construction industry in the adoption of BIM. The methodology has been here classified in four “Levels of Maturity”, that go from 0 to 3; at level 0 there is a complete lack of Building Information Modelling and no collaboration between the different parts is taking place; level 1 implies that 2D and 3D models have been made but collaboration between the parties is not achieved yet; at level 2 the different professionals are collaborating on intelligent data in form of models and possibly additional information, but there is still a lack of a single source of data, and finally at level 3 there is complete and total collaboration in the planning, construction and operational life cycle of the facility and the information are all shared and stored in one single source of data. An idea of the development of the levels is given better in Figure 1.9.
Figure 1.9 Levels of BIM Maturity
Since 2016, the British government has mandated the achievement of BIM level 2 Maturity for all publicly funded construction work.
Other countries where the implementation of BIM is mandatory today for public projects are, amongst others, Norway, Denmark, Finland, Sweden and Singapore. In many others, such the United Arab Emirates or Australia BIM is mandatory for public projects that exceed certain dimensions or costs.
In the United States, BIM isn’t mandated across all the states yet but is expected to grow quickly. In 2010, the state of Wisconsin made it mandatory to implement BIM for public projects if equal or above the total budget of $5 million. Finally, also in Italy in recent times the government has been pushing with ordinances the increase of utilisation of the methodology for public works; since the 1/1/2019, the implementation of BIM is mandatory public works that exceed the budget of 100 million Euros, by 2020 the budget maximum budged was reduced to 50 million, from 2021 it will be
20 of 15M and this value will be further decreased (5.2M in 2022 and 1 million in 2023) until from 2025 it will be mandatory for all public projects.
Some of the leading firms in the BIM software industry are, as of today, Autodesk, producers of e.g.
Revit, Robot, Advanced Steel and Naviswork, and Trimble, whose main products are Tekla and SketchUp. These, as well as other important tools, are illustrated in Figure 1.10. Apart from the more innovative software such as those mentioned above, also more traditional programs like Microsoft Excel and Microsoft Word can obviously be (and usually are) part of the BIM process.
Figure 1.10 List of useful BIM tools
1.4 The case study
The architectonical drawing of the building was handed to me by the company “Leap factory”, with the task of doing a comparison between the performances of two structural materials applied on it, in terms of structural and energetic behaviour. Leap factory is a company based in Turin who built, among others, the “Bivacco Gervasutti” in 2011, as well as other structures in extreme glacial environments like the “frame” project in Greenland. The studied structure that will be presented in the next paragraphs is not a typical bivouac; it is, in dimensions, more of a mixture between a bivouac and a mountain hut (bigger than a usual bivouac but not big enough to be considered a mountain hut, which is usually composed by more than one inside space). However, it is not thought to be managed by a staff living inside of it and providing additional services to the visitors, and its planned function, which is in the end what really matters, is therefore that of a bivouac.
21
1.4.1 Structural framework
As can be observed in Figure 1.11, the structure has a rectangular base of dimensions 6.12x4.8 m.
Three of the four walls are structural, made, depending on the case, of one of the two studied composite materials, which both consist in wooden based panels; a fourth wall, on the short side of the building, is a glass non bearing surface.
Figure 1.11 Floor plan of the building
There are two openings in the form of doors, one placed at the centre of one of the two long sides, the other one on the glass wall, leading to a terrace of dimensions 1.01x4,56m. In ad dition to the panel structure there can be added, if necessary, supporting frames every 1.2m, with a total of six possible frames. The frame system is not associated to any initial pre-dimensioning, it is thought to be added only in case the panels aren’t enough to withstand the whole load the bivouac is subjected to, and therefore to be designed according to the “missing” resistance and stiffness, meaning that which the panels cannot provide. From a more architectonical point of view, the drawing shows a p latform developing from one long side to the other and from the short panel side towards the glass wall for 2.4 m containing five beds, as well as a table allocated more or less at the centre of the internal space and some furniture placed against the long side opposite to the door.
Figure 1.12 illustrates a vertical section and the side view of the structure. The height from the intrados of the floor to the extrados of the ridge of the roof panels is of 4.81 m; as will be explained more specifically in chapter 4, for the creation of the model the thickness of the floor in the drawing
22 has been assumed to be of 12 cm (since not specified), which generates a total height of the frame and of the entire structure of 5.05 m. It can be acknowledged, observing both drawings, first that the two walls on the long sides are of different heights, and second that the door is placed on the smaller wall.
Figure 1.12 From left to right: cross section and side view of the building
The two long walls are one of height 2,28 m (left on the left drawing) and the other of height 3,48 m (right on the left drawing). The view of the cross section also allows to better recognise the supporting frame, composed by four elements, two columns and two rafter beams. One c an also notice three levels at different heights which represent the platforms containing the beds, five on the first two and four on the last one, making a total of fourteen beds.
Figure 1.13 Front view of the building
23 Figure 1.13 shows a view of the building as if one were to stand in front of the glass wall. One can see the geometry of the frame supporting the glass surface, composed by elements of non-specified dimensions.
1.4.2 Setting of the structure
The studied structure doesn’t have a specific location; it is placed in a generic point in the high altitudes of the alpine areas in Italy. A consideration to be made, at this point, concerns the problem of what can be considered “high” alpine environment. In fact, this denomination is not clearly defined, as it could, purely theoretically speaking, vary depending on the latitude of the area, the climate and other factors involved; nevertheless, for the sake of simplicity we will consider at high altitude those environments above 2500 m amsl.
In the case of this building, the company probably originally sent the drawings to the CAI section of Desio, as a keen eye will spot in Figure 1.11, which is a municipality situated in the Lombardy region, so the first intention was perhaps to build it somewhere in the Lombard Alps. However, the indications for this study from the company were to consider it to be at an altitude of 3000 m above the sea level, but no more specific information were given since it was of no particular advantage and therefore interest to give it an exact location. In any case, for the generation of e.g. temperature effects on the model, the building has been given a certain exposition; the glass is facing west, the higher longer wall faces south, and so on.
24
Chapter 2 2D BIM: description of the structural panels and definition of the loads on the structure
The study of the structure was conducted with two different wooden based panels; one is produced by the British company “KINGSPAN”, it is a traditional SIP (structural insulated panel), composed of two OSB sheets separated by one layer of insulation material called PUR. The second on the other hand is composed by an internal layer of LVL wood, a sheet of PUR insulation and one external layer of OSB wood and is produced by a company from Estonia called “PANELO”. Apart from the difference in the purely material composition of the panels, they are also characterized by two different overall thicknesses, resulting in unalike values of stiffness, resistance and thermal conductivity. The first part of this chapter will see a detailed description of those construction systems, while the second one will see, in order to conclude the second BIM dimension described in paragraph 1.3.2, the definition of the loads applied on the examined structure for the structural study.
2.1 What are SIPs?
Structural insulated panels are a form of sandwich panels, consisting of two structural faces and an insulating foam core sandwiched in between them. They are a high-performance building system for light construction developed during the first half of the last century in the United States, and while they are not particularly common in western Europe, they are an often adapted solution in north America and in Russia. The structural faces are usually made of OSB (oriented strand board) wood, but can in some cases also be sheet metal, cement or other types of timber like plywood or LVL (laminated veneer lumber), and the core is typically rigid Polyurethane (PUR), polyisocyanurate (PIR), polystyrene foam (EPS) or extruded polystyrene (XPS) and is significantly thicker than the structural layers. The structural properties of SIPs correspond to those of a I-beam or I-column, where the insulating layer works as a web and the two faces as the flanges (Figure 2.1); the axial and bending forces are therefore carried by the outer layers (the flanges) and the shear force by the core (the web).
To connect one panel to the other there are different options; one is to use timber posts, dimensioned to fit in between the elements, which also work as a reinforcement for the structural purpose of the panel; the problem related to this solution is that the timber creates a thermal bridge, since its conductivity values are much higher than those of the isolation material. To prevent this connection
25 splines can be utilised, usually slightly thinner that the panel (thickness equal to that of the insulation), but equally composed by two structural (OSB) sheets and an insulation core.
Figure 2.1 Typical sandwich plate; sign convention, stresses and internal stress resultants
2.1.1 Benefits and drawbacks
SIPs are very quick and quite easy to install, so much so that the placing of all the required p anels for one entire house can last just two or even one day. They are generally considered to be a lightweight material, but are nevertheless heavy enough for it to be unlikely that one person alone is able to install them unless he/she is equipped with some mechanical arm, therefore usually a crew of people is necessary to build a house. Compared to a traditional timber stick framing construction system, SIPs have much better thermal insulation properties, as the timber elements in the framing system represent a thermal bridge, but they are also generally more expensive; although if one would be taking into account savings related to construction speed and smaller heating and cooling costs, SIPs could very well be just as or probably less expensive than stick framing in terms of total cycle costs. The main difference which in this evaluation often makes people opt for the framing system, is that while in framing construction one can buy one piece at a time and spread the costs more over time, in SIPs one necessarily has to buy the whole piece at once, inevitably making it a higher immediate expense.
Moreover, an OSB skinned SIP structurally can outperform stick framed constructions in the case of axial load strength. A significant throwback of SIP panels is related to moisture, in the form of creation of interstitial condensation in between the layers during the heating season. This is due to the fact that, during the winter, water vapor tends to migrate from the warmer inner environment towards the colder outside. In case of SIPs however, especially the external OSB layer has a too low
26 permeability, causing the water vapor to be subjected to a “blocking” effect and condensate. Finally, a downside of SIP panels that particularly affected this thesis is that there’s no real standardization of them in Italy. Therefore, in the case the considered structure, their analysis was conducted with the use of the CNR-DT-206-R1-2018, which is a general standard for the design of wood, and a PDF file made by the Italian section of a wood promotion initiative of the Austrian company “pro:Holz” called promo_legno. The name of the PDF is “Il calcolo dell`XLAM. Basi, normative, progettazione, applicazione” and, as the title suggests, it actually concerns another type of wooden based panels, namely the crosslams (in Italy often referred to as XLAM), which now won’t be illustrated in detail but in many aspects can be considered similar to the SIPs, at least in the initial approach.
2.2 The KINGSPAN system
The Kingspan panel is called “Kingspan TEK”; as mentioned in the first paragraph of chapter 2, it consists in two faces of OSB and an insulation core of PUR insulation. OSB stands for oriented strand board, and is a type of wood obtained by adding adhesives and then compressing together wood strands in a specific orientation, while PUR stands for rigid polyurethane; it is a polymer, which in this case, as the name suggests, comes in a rigid form. For what concerns the OSB, there are 5 classes of boards: OSB/0 doesn’t have any added formaldehyde, which is one of the components forming the adhesive resins, OSB/1 and OSB/2 are to be used only in dry conditions (the difference relies in the load bearing capacity) and OSB/3 and 4 can be used in humid conditions, where OSB/4 is a heavy duty load-bearing board while OSB/3 is a regular load-bearing board; in the case of the Kingspan panel, the employed class is OSB/3. Regarding the standard characteristics of the panel concerning the thicknesses of the layers, dimensions etc, the datasheet made available by the company will be quoted (BBA Certificate, pag. 5): “Each panel of the Kingspan TEK Building System is nominally 142 mm or 172 mm thick overall and has two outer skins of 15 mm thick OSB/3 (oriented strand board type 3), separated by a core of 112 mm or 142 mm thick, zero rated ozone-depleting potential (ODP) rigid urethane insulation (PUR). The panel mass is approximately 25 kg m^2 for the 142 mm and 172 mm thick panels. The panels are available in widths ranging from 200 mm to 1220 mm, and lengths up to 7500 mm. The panels are supplied in the appropriate shapes and sizes for each project, together with any expanding urethane sealant, fixings and jointing pieces that may be required.
[…]
In addition to the panels, a number of other components are required to facilitate the assembly of the system:
For the 142 mm thick panels:
27
• edge timbers — minimum 50 by 110 mm C16 graded or equivalent (+1/-1 tolerance on dimensions)
• structural timber posts — minimum 100 by 110 mm C24 graded or equivalent
• insulated splines — 100 mm (w) by 110 mm (d), comprising two OSB/3, 15 by 100 mm skins and rigid urethane insulation core (…).
For the 172 mm thick panels:
• edge timbers — minimum 38 by 140 mm C16 graded or equivalent (+1/-1 tolerance on dimensions)
• structural timber posts — minimum 80 by 140 mm C24 graded or equivalent
• insulated splines — 80 mm (w) by 140 mm (d), comprising two OSB/3, 15 by 80 mm skins and rigid urethane insulation core (…).”
Figure 2.2 View of the panels connected by an insulated spline
Of the two possible panel sizes in terms of thickness (142 and 172 mm) described by the datasheet, the one chosen to perform the work was the TEK 142 mm system. This was done for the simple reason that the Kingspan company provides significantly more information related to the connection types to be used and to the standard details of the panel, all of which is of great help when dealing with BIM software and in general with structural design; accordingly, the composition of the panel is of 15 mm OSB, 112 mm PUR and 15 mm OSB.
The characteristics exposed in the next paragraphs regard the system’s strength and stability, the thermal performance, the vapour permeability and the condensation risk of the system as well as the construction details and were all taken from a different documents made public by the company: a certificate awarded by the BBA (British Board of Agrément) and approved by the ETA (European Technical Assessment) which are the UK and EU leading construction certification bodies, a brochure of the panel, and a specification manual of the TEK system.
28
2.2.1 Mechanical properties
The exact density of the different components of the TEK 142 system is provided by the BBA certificate (Table 2.1), same goes for the strength, resistance and stiffness values, that will be illustrated in different Tables and commented throughout the paragraph.
Table 2.1 Density of panel components
The density values were used, in relation to the thickness of the layers, to calculate on excel the total density and self-weight in 𝑘𝑁
𝑚3 of the panel.
Table 2.2 Density and selfweight of the panel
Table 2.3 shows contains the design values of strength that should be compared to the worst loa ding case in the Ultimate Limit State (ULS).
Table 2.3 Structural properties - limit state design - TEK 142
t [mm] ρ [kg/m^3] m [kg/m^2] γtot, KS [kN/m^3]
OSB (ext) 15 650 9,75 /
PUR 112 35 3,92 /
OSB (int) 15 650 9,75 /
TOT,KINGSPAN 142 164,9295775 23,42 1,617959155
29 In addition to providing the typical bending, axial and shear strength and the stiffness, the given table also contains values describing the panel’s racking resistance, which defines its in-plane lateral strength. More specifically, racking occurs when a wall (or panel in this case) is forced out of plumb and tilts due to high horizontal forces usually caused by wind or po ssibly also seismic actions; it is strictly related to the type connections involved, hence the specifications regarding the nail dimensions. In general, the layout of the data emphasizes the difference of strength values according to the duration of the load or, in the case of axial force, to the height of the wall.
According to the EC5, the NTC2018 and the CNR (specific for wood) the definitions of permanent, long, medium short term and instantaneous loads are the following:
-Permanent: more than 10 years
-Long-term: between 6 months and10 years -Medium-term: between one week and six months -Short-term: between one hour and one week -Instantaneous: less than one hour
From a practical point of view, all the values which can be seen in Table 3 basically can be taken as they are, without further calculations, and be used to verify the stability of the panel in the studied case by comparing them with the calculated acting forces. To compute these forces, the arguably most important feature that must be known is the stiffness of the system, which is also given in Table 2.3 but can be observed, along with the shear modulus and the values of kdef, more in detail in another table (Table 2.4) provided by Kingspan. The kdef term is a factor taking into account the increase of deformability with time due to both creep and moisture content of the material. It is useful to determine the reduced stiffness, to be used in order to find the final deformation in the serviceability limit state, in the following way:
𝐸𝐼𝑑,𝑓𝑖𝑛= 𝐸𝐼𝑑
(1+𝑘𝑑𝑒𝑓) (2.1)
Where 𝐸𝐼𝑑 is the design value of the bending rigidity of the material and 𝐸𝐼𝑑,𝑓𝑖𝑛 is the reduced stiffness.
Table 2.4 Bending and shear rigidity of the panel
30
2.2.2 Thermal performance
Regarding the thermal performance of the TEK 142 system, the datasheets come up with various information. In order to calculate the thermal transmittance (U) of the panel, the BBA certificate gives the thermal conductivity (λ) values that should be used, shown in Table 5, or alternatively, the total panel’s thermal resistance (R), in this case given for the whole system. The thermal conductivities of Table 2.5 have unit measure 𝑊
𝑚𝐾 and fundamentally describe a material’s tendency to conduct heat;
the greater they are, the less the material is isolating. The value related to solid timber refers to the structural posts, which can potentially be used as a reinforcement for the panel.
Table 2.5 Thermal conductivities of the TEK Kingspan components
The thermal resistance R values can be observed in Table 2.6, as a function of the panel thickness.
They are computed using spline connections and not timber posts.
Table 2.6 R values of the system
Additionally to the above described layers, another document uploaded by the Kingspan company called “TEK specification manual” states that “All Kingspan TEK® Building System panels should be lined internally with plasterboard” (pag.13), adding a minimum thickness of 12.5 mm and a conductivity λ equal to 0.25 𝑊
𝑚𝐾.
An example of thermal transmittance of a TEK system with an additional layer of Plasterboard of 15 mm, as well as other elements is provided by the BBA certificate and shown on Table 2.7.
Table 2.7 Example panel thermal transmittance
31 Hence, an approximated calculation of the panel’s thermal transmittance U both including and excluding a 15 mm layer of plasterboard and without the employment of timber elements was performed, to make a comparison with the value given by the BBA certificate. Th is was done through the relation:
𝑈 = 1 1
ℎ𝑖+∑ 𝑠𝑖
𝜆𝑖
𝑛𝑖=1 +∑ 𝑅𝑘+1
ℎ𝑒 𝑚𝑗=1
(2.2)
where 𝑛 is the number of homogeneous layers of thickness 𝑠 and thermal conductivity 𝜆, 𝑚 the number of non-homogenous layers for which a thermal resistance 𝑅 is defined, ℎ𝑖 is the internal heat transfer coefficient and ℎ𝑒 the external heat transfer coefficient, both of the latter terms being given by the summation of a convective and a radiation component.
The coefficients ℎ𝑖 and ℎ𝑒 were chosen, according to what literature gives as common values, respectively to be 8 and 25 𝑊
𝑚2𝐾.
The values of s and λ for the respective layers were put in an excel table and the computation was made as can be seen in Tables 2.8 and 2.9.
Table 2.8 Example of calculation of the thermal transmittance U with 15 mm plasterboard
Table 2.9 Example of calculation of the thermal transmittance U witho ut 15 mm plasterboard
It can be noticed both how the values on Table 2.8 and 2.9 for the 142 panel don’t differ much from those given as standard by the company, and also how the thermal transmittance doesn’t change relevantly between with and without the 15 mm plasterboard; this is due to the fact that the most important factor influencing the U value is the insulating core and not the other layers.
Further data provided by the Kingspan company consists in an exposure of other different U values in function of the thickness of a hypothetical additional insulation layer that can be added to the panel system as well as different types of claddings that could be used. Here it will be shown only the case of a ventilated timber cladding, illustrated in Figure 2.3.
s [m] λ [W/mK] UKINGSPAN [W/(m^2*K)]
Plasterboard 0,015 0,25
OSB 0,015 0,13
PUR 0,112 0,024
OSB 0,015 0,13 0,195219622
s [m] λ [W/mK] UKINGSPAN [W/(m^2*K)]
OSB 0,015 0,13
PUR 0,112 0,024
OSB 0,015 0,13 0,197533365
32
Figure 2.3 TEK system with ventilated timber cladding
The thermal transmittances in function of an additional insulation layer are shown in Table 2.10. In this specific case, the Table refers to an insulation board called Kingspan Thermawall® TW55.
Table 2.10 U values in function of thickness of TEK and thermawall
2.2.3 Vapour diffusion and condensation risk
To study the diffusion of water vapour inside the panel, originated by the difference in vapour pressure between the internal and external environment, the BBA certificate provides, similarly to the case of thermal conductivity, the values to be used when performing a calculation of the possible condensation point. In this case, the given quantities are those of the vapour diffusion resistance factor μ, which are dimensionless.
33
Table 2.11 Vapour diffusion factor of the TEK components
Fundamentally, those values show how much more resistance a material applies to the diffusion of vapour inside of it with respect to air. In fact, to derive the material’s permeability given its diffusion resistance factor, one puts in relation the latter to the air permeability, in the following way:
𝛿𝑖 =𝛿0
𝜇 (2.3) where:
-𝛿𝑖 is the material’s vapour permeability in 𝑘𝑔
𝑚2∗𝑃𝑎∗𝑠,
-𝛿𝑜 is the vapour permeability of air equal to approximately 2 ∗ 10−10 𝑘𝑔
𝑚2∗𝑃𝑎∗𝑠, -𝜇 is the vapour resistance of the material.
Knowing the permeabilities, one can easily compute the total vapor diffusion resistance of the wall 𝑅𝑣, defined in 𝑚2∗𝑃𝑎∗𝑠
𝑘𝑔 , with the formula:
𝑅𝑣= 1
𝛽𝑖+ ∑ 𝑠𝑖
𝛿𝑖+ 1
𝛽𝑒
𝑛𝑖=1 (2.4)
being n the number of layers of the wall, 𝑠𝑖 the thickness of the layer, 𝛿𝑖 the vapour permeability of the layer and 𝛽𝑖 and 𝛽𝑒 the water vapour transfer coefficients, whose value is so high that the first and last term of the equation can be assumed equal to zero. Therefore,
𝑅𝑣= ∑ 𝑠𝑖
𝛿𝑖
𝑛𝑖=1 (2.5)
From the vapour resistance, one can compute the permeance of the wall, which is simply the inverse of the resistance:
𝑀 = 1
𝑅𝑣= 1
∑ 𝑠𝑖
𝛿𝑖 𝑛𝑖=1
(2.6)
It conceptually describes the ease with which water vapour molecules diffuse through the wall.
However, as mentioned in paragraph 2.1.1, SIP panels generally are at high risk of interstitial condensation, since they tend to “trap” the vapour which creates moisture. In fact, the “TEK specification manual” states that “If a condensation risk is predicted, it can be controlled by ensuring there is a layer of high vapour resistance on the warm side of the insulation layer. If required, the vapour resistance of the wall lining can be increased by the use of a vapour check plasterboard*; the use of Kingspan Thermapitch® TP10 or Thermawall® TW55, both of which contain an integral vapour control layer*; the use of a layer of polythene sheeting*; or by the application of two coats of Gyproc Drywall Sealer to the plasterboard lining” (pag.12).
34 In general, when trying to control interstitial condensation, it is always a good rule to place materials with decreasing water vapour resistance from the inside out.
Following the indications of the manual, a calculation of the vapour resistance and of the permeance of a wall composed by the Kingspan TEK system and a high vapour resistant plasterboard of thickness 15 mm, and one of a wall composed only by the TEK system were performed on Excel. The results are shown Table 2.12 and 2.13; they have obviously only a pure indicative value, as the humidity conditions the panel is exposed to play a significant role in the evaluation of those values.
Table 2.12 Water vapour resistance and permeance of the wall composed by the TEK system and a 15 mm plasterboard
Table 2.13 Water vapour resistance and permeance of the wall composed only by the TEK system
It can be observed how here, unlike the thermal transmittance case, the plasterboard added to the wall makes a significant difference.
The vapour diffusion resistance factor of the plasterboard was taken from the webpage of a different British company, that produces plasterboards, called “British gypsum”. It provides with the value of the total vapour resistance of a plasterboard named “Gyproc WallBoard Duplex”, but since it obviously follows British literature the value is given in 𝑀𝑁𝑠
𝑔 (Mega-Newton seconds per gram).
Quoting1: “The water vapour resistance of Gyproc WallBoard Duplex is 60MNs/g”. One must multiply it times 109 to obtain the 𝑅𝑣 value in 𝑚2∗𝑃𝑎∗𝑠
𝑘𝑔 or, in order to convert it first into the vapour diffusion resistance factor μ, one has to multiply the original value times 0.2 𝑀𝑁𝑠
𝑔 (which is the value of vapour permeability of still air, equivalent to the 𝛿𝑜 term seen in (2.3)) and then divide it by the thickness of the layer in meters.
1 https://www.british-gypsum.com/technical-advice/faqs/063-what-is-the-vapour-resistance-of-gyproc-wallboard- duplex-plasterboard
μ [-] s [m] λ [W/mK] δ [kg/Pa*m*s] Rv [m^2*Pa*s/kg] M [kg/m^2*Pa*s]
Plasterboard 800 0,015 0,25 2,5E-13 60000000000 1,66667E-11
OSB,int 50 0,015 0,13 4E-12 3750000000 2,66667E-10
PUR 60 0,112 0,024 3,33333E-12 33600000000 2,97619E-11
OSB,ext 30 0,015 0,13 6,66667E-12 2250000000 4,44444E-10
Tot / 0,157 / / 99600000000 1,00402E-11
μ [-] s [m] λ [W/mK] δ [kg/Pa*m*s] Rv [m^2*Pa*s/kg] M [kg/m^2*Pa*s]
OSB,int 50 0,015 0,13 4E-12 3750000000 2,66667E-10
PUR 60 0,112 0,024 3,33333E-12 33600000000 2,97619E-11
OSB,ext 30 0,015 0,13 6,66667E-12 2250000000 4,44444E-10
Tot / 0,142 / / 39600000000 2,52525E-11
